DC machines

A DC machine converts mechanical energy to DC electrical energy (generator) or the reverse (motor). The same machine can do both. Although power electronics has replaced many DC drives, DC machines still appear in traction, cranes, battery-fed systems and as exciters, and their theory — emf equation, armature reaction, commutation, characteristics and speed control — is heavily tested in NEC exams.

Key concepts

• Construction:
  • Yoke: outer frame, mechanical support and return path for flux (cast iron/steel).
  • Poles and pole shoes: carry field winding; shoe spreads flux and supports the coil.
  • Field winding: produces main flux.
  • Armature core: laminated silicon steel drum with slots; armature winding: lap ($A = P$ parallel paths, for high current/low voltage) or wave ($A = 2$, for high voltage/low current).
  • Commutator: copper segments insulated by mica; acts as a mechanical rectifier (generator) or inverter (motor).
  • Brushes: carbon/graphite, collect current from the commutator.
  • Interpoles and compensating windings (in large machines).
• Working principle: generator — conductors cut flux, emf by Fleming's right-hand rule, AC in the coil rectified by the commutator. Motor — current-carrying conductors in flux experience force (left-hand rule); the induced back emf $E_b$ opposes supply voltage and regulates armature current.
• Types by excitation: separately excited; self-excited — shunt, series, compound (cumulative/differential, long/short shunt).
• Generator characteristics:
  • Shunt: voltage builds up only if residual magnetism exists, field connection aids it, and field resistance < critical resistance; speed above critical speed. Terminal voltage falls slightly with load.
  • Series: voltage rises with load (used as boosters).
  • Cumulative compound: flat (level) or over-compounded — used for supply over feeders.
• Motor characteristics:

Motor	Speed–load	Torque	Typical use
Shunt	Nearly constant speed	$T \propto I_a$	Lathes, fans, pumps, conveyors
Series	Speed falls sharply; dangerous at no load	$T\propto I_a^2$ (before saturation), high starting torque	Traction, cranes, hoists
Cumulative compound	Between the two; safe no-load speed	Good starting torque	Presses, shears, rolling mills

A series motor must never be started or run without load (belt drive avoided).

• Armature reaction: effect of armature MMF on main field. It cross-magnetises (distorts flux, shifts the magnetic neutral axis — forward in generator, backward in motor) and demagnetises (with brush shift). Remedies: compensating winding in pole faces, interpoles, high-reluctance pole tips.
• Commutation: reversal of coil current while short-circuited by a brush; delayed reversal (reactance voltage) causes sparking. Remedies: resistance commutation (carbon brushes), emf commutation (interpoles, brush shift).
• Losses: copper (armature, field, brush contact), iron (hysteresis + eddy in armature), mechanical (friction, windage). Constant losses = iron + mechanical + shunt field. Maximum efficiency when variable (armature Cu) loss = constant loss.
• Starting: at standstill $E_b = 0$, so $I_a = V/R_a$ would be very large. A starter adds series resistance which is cut out as speed rises: 3-point starter (shunt motor; no-volt coil in field circuit — opens if field fails), 4-point starter (no-volt coil across supply, independent of field — allows field control). Both have overload release.
• Speed control from $N \propto (V - I_aR_a)/\Phi$:
  • Flux (field) control: rheostat in shunt field — above-rated speed, efficient, constant power.
  • Armature resistance control: below-rated speed, wasteful.
  • Armature voltage control: Ward-Leonard system or modern thyristor/chopper drives — smooth, wide range, both directions.
  • Series motor: diverter across field, tapped field, series–parallel control (traction).

High-yield points

• Emf $E = P\Phi ZN/(60A)$; lap winding $A = P$, wave winding $A = 2$.
• Motor: $V = E_b + I_aR_a$; speed $N \propto E_b/\Phi$.
• Series motor: $T \propto I_a^2$ (unsaturated), highest starting torque, never run on no load.
• 3-point starter's no-volt coil is in series with the field; 4-point starter's is across the supply.
• Maximum efficiency when variable (armature copper) loss = constant loss.
• Field weakening raises speed above rated; armature resistance control gives below-rated speed.

Formulas

$E = \frac{P\Phi Z N}{60A}$ P = poles, Φ = flux/pole (Wb), Z = total conductors, N = speed (rpm), A = parallel paths.

Generator: $V = E - I_aR_a$; motor: $V = E_b + I_aR_a$.

$T = 0.159\frac{P\Phi Z I_a}{A}\ \text{N·m},\qquad N \propto \frac{E_b}{\Phi}$

Worked example

A 220 V shunt motor has $R_a = 0.5$ Ω and draws armature current 20 A at 1000 rpm. Find speed when $I_a = 40$ A (flux constant).

1. $E_{b1} = 220 - 20\times0.5 = 210$ V.
2. $E_{b2} = 220 - 40\times0.5 = 200$ V.
3. $N_2 = 1000\times200/210 = 952$ rpm.

Exam tips

• Lap: A = P; wave: A = 2 regardless of poles.
• Series motor: highest starting torque, never on no load. Shunt: constant speed.
• Field weakening raises speed; armature resistance control lowers speed.
• Back emf is what makes a DC motor self-regulating; starter needed because $E_b = 0$ at start.
• Interpoles are in series with the armature; compensating winding neutralises cross-magnetisation under pole faces.

Exam-style questions

From Calmon's question bank, which has 25 questions on this topic.

1. The armature of a DC motor has a back emf of 200 V and an armature current of 50 A while running at 1000 rpm. The electromagnetic torque developed is about:

• A. 955 N·m
• B. 191 N·m
• C. 95.5 N·m
• D. 10 N·m

Answer: C. $T = E_bI_a/\omega = (200\times50)/(2\pi\times1000/60) = 10000/104.7 \approx 95.5$ N·m.

2. A 220 V DC motor has armature resistance $0.5\,\Omega$. The external resistance needed in the starter to limit the starting armature current to 40 A is:

• A. 0.5 Ω
• B. 5.5 Ω
• C. 5.0 Ω
• D. 4.5 Ω

Answer: C. At start $E_b = 0$: total resistance $= 220/40 = 5.5\,\Omega$, so external resistance $= 5.5 - 0.5 = 5.0\,\Omega$.

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